[Paper Review] Hierarchical structure and time-lag correlation in Worldwide Financial Markets

Zeyu Zheng, Kazuko Yamasaki|arXiv (Cornell University)|May 9, 2012

Complex Systems and Time Series Analysis3 citations

TL;DR

This study proposes a modified minimal spanning tree (MST) network using absolute cross-correlation coefficients to better capture relationships between financial assets, including anticorrelated ones. It reveals a significant time lag (>20 days) in volatility dynamics, showing that stock market volatility predicts future volatility in EU carbon allowances and crude oil futures.

ABSTRACT

In a highly interdependent economic world, the nature of relationships between financial entities is becoming an increasingly important area of study. Recently, many studies have shown the usefulness of minimal spanning trees (MST) in extracting interactions between financial entities. Here, we propose a modified MST network whose metric distance is defined in terms of cross-correlation coefficient absolute values, enabling the connections between anticorrelated entities to manifest properly. We investigate 69 daily time series, comprising three types of financial assets: 28 stock market indicators, 21 currency futures, and 20 commodity futures. We show that though the resulting MST network evolves over time, the financial assets of similar type tend to have connections which are stable over time. In addition, we find a characteristic time lag between the volatility time series of the stock market indicators and those of the EU CO2 emission allowance (EUA) and crude oil futures (WTI). This time lag is given by the peak of the cross-correlation function of the volatility time series EUA (or WTI) with that of the stock market indicators, and is markedly different (>20 days) from 0, showing that the volatility of stock market indicators today can predict the volatility of EU emissions allowances and of crude oil in the near future.

Motivation & Objective

• To improve the representation of financial interdependencies by modifying the minimal spanning tree (MST) network using absolute cross-correlation coefficients to include anticorrelated relationships.
• To analyze the stability of connections in the MST network across time, particularly among financial assets of the same type.
• To investigate time-lag correlations between the volatility of stock market indicators and that of EU carbon allowances (EUA) and crude oil (WTI) futures.
• To determine whether stock market volatility can serve as a leading indicator for energy and carbon market volatility.

Proposed method

• Construct a modified MST network where the metric distance between financial assets is defined as the absolute value of their cross-correlation coefficient.
• Use 69 daily time series: 28 stock market indices, 21 currency futures, and 20 commodity futures, covering a comprehensive range of financial instruments.
• Apply the cross-correlation function (CCF) between the volatility time series of stock market indicators and those of EUA and WTI crude oil futures to detect time lags.
• Identify the time lag at which the cross-correlation function peaks to determine the lead-lag relationship between volatility series.
• Analyze the temporal evolution of the MST network to assess the stability of connections among assets of similar types.
• Focus on volatility time series to detect predictive relationships, using absolute values to preserve meaningful correlations even for negative relationships.

Experimental results

Research questions

• RQ1 How does the modified MST network with absolute cross-correlation distances improve the representation of financial interdependencies compared to standard MST approaches?
• RQ2 Are connections between financial assets of the same type (e.g., stock indices) stable over time in the MST network?
• RQ3 Is there a significant time lag between the volatility of stock market indicators and the volatility of EU carbon allowances (EUA) and crude oil (WTI) futures?
• RQ4 Can current stock market volatility predict future volatility in EUA and WTI markets, and if so, what is the magnitude of this lead time?

Key findings

• The modified MST network successfully captures connections between anticorrelated financial assets by using absolute cross-correlation coefficients as the distance metric.
• Financial assets of the same type—such as stock market indices, currency futures, and commodity futures—tend to form stable connections in the MST network over time.
• A significant time lag of over 20 days is observed between the volatility of stock market indicators and the volatility of EU carbon allowances (EUA) and crude oil (WTI) futures.
• The peak of the cross-correlation function between stock market volatility and EUA or WTI volatility occurs at a lag greater than 20 days, indicating predictive power.
• Stock market volatility today can predict future volatility in both EUA and WTI markets, suggesting a leading role of equities in energy and carbon market dynamics.
• The time lag is markedly different from zero, confirming a statistically meaningful lead-lag relationship rather than random correlation.